Since the global arm can be formed from the combination of the local arms, if we use the naïve assumption [1]}, the global reward \(R_{\rm global}\)  for \(MAB_g\)  can be approximated by the sum of the reward of local MABs, and each local reward only depends on the choice made in each local MAB. This also means that, if the global reward is more easily accessed than the local rewards, then the local rewards can be approximated from the global reward. With the naïve assumption, we can have a linear relationship between the global reward and local rewards:
\(R_{\rm global} = \frac{1}{p}\sum _{i=1}^p R_i\) 
